What is the inverse of the function $f(x)=-6x-7$ ? $f^{-1}(x)=$
Let's start by replacing $f(x)$ with $y$. $y=-6x-7$ If a function contains the point $(a,b)$, the inverse of that function contains the point $(b,a)$. So if we swap the position of $x$ and $y$ in the equation, we get the inverse relationship. In this case, the function is $y=-6x-7$, so the inverse relationship is $x=-6y-7$. Solving this equation for $y$ will give us an expression for $f^{-1}(x)$. $\begin{aligned} x&=-6y-7\\\\ x+7&=-6y\\\\ -\dfrac{1}{6}(x+7)&=y\\\\\\ \end{aligned}$ The inverse of the function is $f^{-1}(x)=-\dfrac{1}{6}(x+7)$. [I saw someone solve this problem by originally solving for x. Were they wrong?]